Extending class group action attacks via pairings

Joseph Macula; Katherine E. Stange

Paper 2024/880

Extending class group action attacks via pairings

Joseph Macula, University of Colorado Boulder

Katherine E. Stange

, University of Colorado Boulder

Abstract

We introduce a new tool for the study of isogeny-based cryptography, namely pairings which are sesquilinear (conjugate linear) with respect to the $\mathcal{O}$-module structure of an elliptic curve with CM by an imaginary quadratic order $\mathcal{O}$. We use these pairings to study the security of problems based on the class group action on collections of oriented ordinary or supersingular elliptic curves. This extends work of of both (Castryck, Houben, Merz, Mula, Buuren, Vercauteren, 2023) and (De Feo, Fouotsa, Panny, 2024).

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Isogeny-based cryptography Pairings Elliptic Curves
Contact author(s): joseph macula @ colorado edu
kstange @ math colorado edu
History: 2024-06-14: revised; 2024-06-02: received; See all versions
Short URL: https://ia.cr/2024/880
License: CC BY

BibTeX

@misc{cryptoeprint:2024/880,
      author = {Joseph Macula and Katherine E. Stange},
      title = {Extending class group action attacks via pairings},
      howpublished = {Cryptology ePrint Archive, Paper 2024/880},
      year = {2024},
      note = {\url{https://eprint.iacr.org/2024/880}},
      url = {https://eprint.iacr.org/2024/880}
}